Cross-traffic alert systems that notify an operator when an approaching vehicle is predicted to pass behind the host-vehicle are known. The prediction can be difficult when, for example, initial heading estimates might be erroneous, and/or the road may be curved. It has been observed that vehicles that are headed for the alert region may appear to be headed away until the last moment, leading to late alerts. It has been proposed to fit trajectories of approaching vehicles with a polynomial or other curved least-squares model. However, this solution may excessively tax the available computing resources and require large amounts of memory to store data and solutions more than a small number of past trajectories.